What is the limit as x approaches infinity of (1-0.8^{x+1})/(1-0.8) ?

The limit as x approaches infinity of (1-0.8^{x+1})/(1-0.8) is 5

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limit as x approaches infinity of (1-0.8^{x+1})/(1-0.8)

x \to \infty lim (\frac{1 - 0. 8 ^{x + 1}}{1 - 0.8})

5

Solution steps

x \to \infty lim (\frac{1 - 0. 8 ^{x + 1}}{1 - 0.8})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{1 - 0.8} \cdot x \to \infty lim (1 - 0. 8^{x + 1})

Simplify

= 5 \cdot x \to \infty lim (1 - 0. 8^{x + 1})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= 5 (x \to \infty lim (1) - x \to \infty lim (0. 8^{x + 1}))

x \to \infty lim (1) = 1

x \to \infty lim (0. 8^{x + 1}) = 0

= 5 (1 - 0)

Simplify

= 5

\frac{3}{( s - 3 )}

\frac{\partial}{\partial y} ((x + 2 y^{3})^{\frac{1}{3}})

\int_{0}^{l n (3)} x e^{x} d x

f (x) = - 2 x e^{- x^{2}}

\int \frac{1}{( y - 1 ) ^{2}} d y

What is the limit as x approaches infinity of (1-0.8^{x+1})/(1-0.8) ?
The limit as x approaches infinity of (1-0.8^{x+1})/(1-0.8) is 5